Ms Wintour is under consideration for the role of U.S. ambassador but would need the President's nomination.

Louis Susman, the current Ambassador to the Court of St. James's, was appointed in 2009 but has said that he will step down from the post.

But Mr Bryan's alleged tax woes could put her chances in jeopardy.

He grabbed headlines last month when he suggested the Old Boys' Club of politics
is unwilling to let the British-born publishing maven into their ranks
despite her business acumen and successful fundraising efforts for Obama.

The Vogue editor was born in London, a
daughter of Charles Wintour who edited the London Evening
Standard.

The
fashion queen became a U.S. citizen and has been active in politics and an ardent supporter of Mr Obama's, including holding a $35,000 a head fundraising dinner in August. In his speech Mr Obama thanked 'Anna and Shelby for being such extraordinary hosts'.

She also championed an Obama fundraiser at Paris
Fashion Week and was among the hosts at a London party for the
Democrat.

Woman in charge: Wintour is rumored to be on President Obama's short list to be the U.S. ambassador to Great Britain

The head of the Condé Nast
publication also enlisted her celebrated designer friends to create
Obama-themed paraphernalia, for the Runway to Win campaign, so supporters could fashionably show their support for the president. The effort raised $40 million.

With her long-list of political good
deeds, alongside her business CV of running a multimillion-dollar
magazine, Bryan says it is unfair that the media exec, dubbed 'Nuclear Wintour,'is not being given due credit based on her merits.

‘It’s a little bit of male chauvinism,’ he said.

‘It’s
not just Anna - I see powerful women who really get slammed for being
too forthright or running their business in a very determine way.’

'I think she would do a great job if
it ever happened, but I’m not expecting it to happen,' Bryan said about
the reports, adding that she already has a good gig going.

'She has a great job at Vogue that she loves very much. So I don’t know about that.'